Letters

On a related point, I note that Berlinski casts himself as "a forthright defender of the reptile to mammal sequence". I would like to know if he can cite a single article, letter or internet post of his whose net effect is to defend the sequence. I exclude any articles taking the line "I support the reptile-mammal sequence but here are some arguments against it", whose net effect is to undermine the position rather than defend it. Indeed, I believe that is their purpose. I doubt that Berlinski has ever been a forthright defender, and suggest that he presents himself as such only to strengthen the effect of his contrary innuendo on the impressionable reader: if even a forthright defender of the sequence is starting to have doubts about it, then the mainstream interpretation must be in trouble! In other words, the claim to be a defender of the sequence is just another rhetorical device.

David Berlinski writes "... there is no indication in their paper that the calculations had been given to the Proceedings of the Royal Society of London, nor in the ten years since the publication of their paper have Nilsson and Pelger ever made their calculations available in any public format whatsoever. With this in mind I entertained the hypothesis – I did not nothing more – that Nilsson and Pelger had not performed those calculations for the full range of their sequence, but had instead undertaken calculations for a handful of points and completed their sequence by extrapolation. Whether this is what they did, I wrote, was something that I did not know."

He seems to have underestimated the force of his prose. In fact he wrote:
"Moreover, Nilsson and Pelger do not calculate the visual acuity of any structure, and certainly not over the full 1,829 steps of their sequence. They suggest that various calculations have been made, but they do not show how they were made or tell us where they might be found. At the very best, they have made such calculations for a handful of data points, and then joined those points by a continuous curve."

and:
"As I have already observed, the number 363,992 is derived from the number 80,129,540, which is derived from the number 1,829-which in turn is derived from nothing at all."

In fact, Nilsson and Pelger are very clear where the 1,819 steps come from, and very clear about the source of their calculations. Figure 1 (page 54) of their article consists of three graphs. The first shows increase of spatial resolution as the light sensitive patch invaginates (model sequence steps 1 to 3). The text commenting on this graph refers us to Nilsson 1990 for further details.

The second graph shows improvement of detectable resolution as the appature narrows when pit depth equals diameter (model sequence steps 3 to 6). The text cites two papers and the equation used to calculate this (and, I believe, the previous) graph.

The third graph plots increase of optical resolution as the refractive index of the lense increases. Again the text cites the source of the equations used (Fletcher et al. 1954).

So though figure three only plots the optical performance of the first seven model eyes, the performance of the continuos range of intermediate eyes has been previously plotted in figure 1.

Finaly, had Berlinski been in doubt as to the treatment of the subject, or the exact source of the various figures, he need only have written one of the authors and asked. As Berlinski has written to Nilsson on a related matter, such an enquiry would only be polite before making accusations of fraud.